Mechanics, Analysis and Geometry: 200 Years After Lagrange

Title......Page 1
Foreword......Page 3
Part I. Dynamical systems......Page 11
Dell\'Antonio G. Periodic solutions near the Lagrange equilibrium points in the restricted three-body problem, for mass ratios near Routh\'s critical value......Page 13
Ghidaglia J.-M., Temam R. Lower bound on the dimension of the attractor for the Navier-Stokes equations in space dimension 3......Page 43
Holm D.D., Kovacic G. Homoclinic chaos for ray optics in a fiber: 200 years after Lagrange......Page 71
Marchioro C. , Pulvirenti M., Lagrange J.L. On the vortex–wave system......Page 89
Part II. Integrable systems and quantum groups......Page 107
Krichever I.M. The averaging procedure for the soliton-like solutions of integrable systems......Page 109
Fomenko A.T. A new topological invariant of topological Hamiltonian systems of differential equations and applications to problems in physics and mechanics......Page 137
Zakharov V.E. On the Lie algebra of motion integrals for two-dimensional hydrodynamic equations in Clebsh variables......Page 167
Kupershmidt B.A. Quasiclassical limit of quantum matrix groups......Page 181
Part III. Analytical mechanics and calculus of variations......Page 211
Gotay M.J. A multisymplectic framework for classical field theory and the calculus of variations......Page 213
Kalnins E.G., Levine R.D., Miller Jr. W. Conformal symmetries and generalized recurrences for heat and Schrödinger equations in one spatial dimension......Page 247
Shadwick W.F. On the geometry of the Lagrange problem......Page 267
Part IV. Global analysis......Page 287
Avez A. Massivité des espaces de sobolev et spectre du Laplacien des variétés riemanniennes compactes......Page 289
Choquet-Bruhat Y. Yang-Mills fields on Lorentzian manifolds......Page 299
Rassias T.M. Eigenvalues of the Laplacian......Page 325
Part V. Differential geometry......Page 343
DeTurck D., Gluck H., Gordon C., Webb D. How can a drum change shape, while sounding the same?......Page 345
Hitchin N. Vector fields on the circle......Page 369
Vinogradov A.M. Scalar differential invariants, diffieties and characteristic classes......Page 389
Part VI. Relativity and field theory......Page 425
Ashtekar A., Bombelli L., Reula O. The covariant phase space of asymptotically flat gravitational fields......Page 427
Ferraris M., Francaviglia M. The Lagrangian approach to conserved quantities in general relativity......Page 461
Fré P. Differential geometry and the Lagrangians of superstring theory......Page 499
Nelson J.E., Regge T. Quantum gravity and quantum groups......Page 513
Penna V., Rasetti M., Spera M. Chen\'s iterated path integrals, quantum vortices and link invariants......Page 523
Stelle K.S. Massive modes and effective geometry......Page 537
Part VII. History of mathematics......Page 557
Dieudonné J. Formal versus convergent power series......Page 559
Author Index......Page 569